Donald Trump has said the ceasefire agreement with Iran is "over", blasting the country's leadership as "scum" and "cuckoo" after fresh exchanges of fire overnight.

Speaking later to reporters at a Nato summit in Turkey, the American president said the US "hit them very hard last night" and will "probably hit them hard again tonight".

He accused Tehran of violating an interim deal signed by both countries in June that called for an end to the conflict, adding that they "lie" and "cheat".

Iran's Foreign Minister Abbas Araghchi responded in a post on X: "We do not answer vulgarity with vulgarity, but with action: fearlessly and with great valour."

Tuesday night into Wednesday saw the worst exchange of strikes between the US and Iran since the deal - known as a memorandum of understanding (MoU) - was signed on 17 June.

It included 14 points, among them a 60-day period for a ceasefire during which negotiations should continue, the safe passage of vessels through the Strait of Hormuz and the US lifting sanctions on Iran.

When asked about the deal at the Nato summit on Wednesday, Trump said: "I think it's over. I don't want to deal with them any more, they're scum... they're led by sick people and they're vicious, violent people."

"We make a deal... They [Iran] go outside, talk to the press, they say 'we never even talked about it'. There's something wrong with them. They're cuckoo. As far as I'm concerned, it's over."

Speaking ahead of the summit, the president said US negotiators could continue talks "if they want" but said he saw it as "a waste of time".

However in a later news conference, Trump told reporters he didn't think the Iran war would start again and said "anything that happens will be over quickly".

His comments have prompted responses from several Iranian officials. A senior adviser to Iran's supreme leader, Ali Akbar Velayati, warned new strikes from the US would be met with an "immediate response".

Iran's Deputy Foreign Minister Kazem Gharibabadi also said Trump's comments "are not a sign of strength, but rather an admission of the failure of a policy built on brute force, sanctions, and threats for years, which could not bring the Iranian nation to its knees".

US Central Command (Centcom) said on Tuesday it had launched "powerful" strikes in response to attacks on three tankers in the Strait of Hormuz. Iranian state media said eight members of the country's army had been killed in US strikes in Bandar Abbas and Bushehr, southern Iran.

The US also said it had revoked its temporary suspension of sanctions on Iranian oil sales.

On Wednesday, Iran said it targeted US military sites in Bahrain and Kuwait in retaliation.

Oil prices jumped after Trump's comments, although they are still well below the highs seen during the full closure of the strait.

Centcom said on Wednesday more than 20 US Navy warships were continuing to patrol waters across the Middle East.

Iran's parliamentary speaker Mohammad Bagher Ghalibaf, who is also the country's chief negotiator with the US, accused the US of breaching the MoU on sanctions on oil sales and other issues, including the attacks in southern Iran and "violating Iranian adjustments in the Strait".

"The era of bullying and extortion is over. It leads nowhere. We don't fold," he said after the US strikes.

Nato chief Mark Rutte described the American strikes as "absolutely necessary", saying that Iran was "basically violating the ceasefire".

There have been several exchanges of fire since the MoU was signed last month.

The US launched a series of strikes on Iran on 26 June after an Iranian projectile hit a cargo ship in the Strait of Hormuz. Further US strikes took place on 27 June, following an attack on a tanker. But later that month both sides had agreed to "stand down".

Part of the MoU's 14 points is for an "immediate and permanent termination of military operations on all fronts".

Iran agreed to use its "best efforts for the safe passage of commercial vessels with no charge for 60 days".

Both sides had continued negotiations on the terms of a permanent end to the war, but talks were paused during funeral ceremonies for the late Ayatollah Ali Khamenei, who was killed on the first day of US-Israel strikes on Iran.

Ceremonies are taking place in Iraq on Wednesday, with the final rites and burial set for Mashhad in north-east Iran on Thursday.

It is not clear when talks will resume after this latest round of strikes, as Trump responded to a question about further negotiations with the comment: "I don't care".

"Frankly, I don't want to waste my time with them. Now, I'll let our wonderful negotiators keep talking if they want, but I don't see it," Trump said.

Trump also referenced his special envoy Steve Witkoff and son-in-law Jared Kushner, calling them "good people" who could negotiate if they wanted to. The pair previously played a role in peace talks.

"I'll speak to our negotiators, if they want to negotiate they're good people - Steve Witkoff, Jared Kushner - but they have to come back to me, as far as I'm concerned it's just a waste of time."